Assessing the parameterisation of the settling flux in a depth-integrated model of the fate of decaying and sinking particles, with application to fecal bacteria in the Scheldt Estuary

The fate of reactive tracers is often modelled by depth-averaged equations. When integrating the depth-resolved equations, it appears that the term describing the settling of particles is dependent on the concentration just above the bottom. Because in a depth-averaged framework this quantity is not available, the settling term needs to be parameterised. The most natural choice is to make the settling flux dependent on the average concentration. This approximation is acceptable if the water column is well mixed, but these conditions are not necessarily met in real applications. Therefore, this study aims at assessing and understanding the error made by using a depth-averaged model in a range of realistic conditions. For the definition of these conditions, typical values for the Scheldt Estuary and the Dutch-Belgian coast were taken. The realistic inspiration for the reactive tracer in this study is the fecal bacterium Escherichia coli, whose own dynamics are characterised by settling and gradual decay by mortality. In an attempt to understand the relative importance of several factors like settling, mortality, mixing and stratification on the error made by a depth-averaged approach, a number of simplified test cases were investigated. It follows that, as expected, the error is acceptable if the situation is mixing-dominated. However, the effect of mortality and stratification was less obvious in advance. For instance, it appeared that errors can also be significant if settling and mortality have the same characteristic timescales. Stratification often has the effect to increase the error made by the depth-averaged model.